Linear System and Response

The performance of fluorescence detectors in capillary electrophoresis is maximized when the excitation light intensity is modulated in time with optimal frequencies. This is especially true when photomultiplier tubes are used to detect the fluorescent light. The photomultiplier tube amplified raw output signal can in principle be captured directly by a personal computer sound card (PCSC) and processed by a lock-in emulated by software. This possibility is demonstrated in the present work and the performance of this new setup is compared with a traditional data acquisition system. The results obtained with this "PCSC and lock-in emulated by software" were of the same quality or even better compared to that obtained by conventional time integrators (Boxcars) and data acquisition boards. With PCSC the limits of detection (LOD) found for both naphthalene-2,3-dicarboxaldehyde-derivatized tyrosine and alanine were 3.3 and 3.5fmol (injection of 5nL of samples at 0.66 and 0.70micromol/L), respectively. This is at least three times better compared to conventional systems when light emitting diodes (LEDs) are used as the excitation source in fluorescence detectors. The PCSC linear response range was also larger compared to conventional data acquisition boards. This scheme showed to be a practical and convenient alternative of data acquisition and signal processing for detection systems used in capillary electrophoresis.

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.